The causal bootstrap computes rigorous bounds on smeared spectral functions from non-perturbative Euclidean data by optimizing over the convex set of compatible positive spectral densities and reducing dual problems to semidefinite programs for certain kernels.
Transport Properties of the Quark-Gluon Plasma -- A Lattice QCD Perspective
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abstract
Transport properties of a thermal medium determine how its conserved charge densities (for instance the electric charge, energy or momentum) evolve as a function of time and eventually relax back to their equilibrium values. Here the transport properties of the quark-gluon plasma are reviewed from a theoretical perspective. The latter play a key role in the description of heavy-ion collisions, and are an important ingredient in constraining particle production processes in the early universe. We place particular emphasis on lattice QCD calculations of conserved current correlators. These Euclidean correlators are related by an integral transform to spectral functions, whose small-frequency form determines the transport properties via Kubo formulae. The universal hydrodynamic predictions for the small-frequency pole structure of spectral functions are summarized. The viability of a quasiparticle description implies the presence of additional characteristic features in the spectral functions. These features are in stark contrast with the functional form that is found in strongly coupled plasmas via the gauge/gravity duality. A central goal is therefore to determine which of these dynamical regimes the quark-gluon plasma is qualitatively closer to as a function of temperature. We review the analysis of lattice correlators in relation to transport properties, and tentatively estimate what computational effort is required to make decisive progress in this field.
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A kernel-derived orthogonal basis enables controlled approximation of spectral functions and low-energy transport coefficients from Euclidean correlators without priors.
Lattice QCD results show the shear viscosity to entropy density ratio of gluon plasma reaches a minimum near the transition temperature Tc while the bulk viscosity to entropy density ratio decreases monotonically from 0.76 to 2.25 Tc.
Authors derive new Kubo formulae for transport coefficients by analyzing analytic structures of stress-energy response functions in second- and third-order hydrodynamics.
In SU(2) lattice QCD at finite density, the chiral magnetic effect from axial-vector correlators remains close to the free massless quark value with weak T and mu dependence in the plasma, while negative magnetoresistance from vector correlators is strongly suppressed at high density or temperature.
citing papers explorer
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The Causal Bootstrap: Bounding Smeared Spectral Functions from Non-Perturbative Euclidean Data
The causal bootstrap computes rigorous bounds on smeared spectral functions from non-perturbative Euclidean data by optimizing over the convex set of compatible positive spectral densities and reducing dual problems to semidefinite programs for certain kernels.
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A kernel-derived orthogonal basis for spectral functions from Euclidean correlators
A kernel-derived orthogonal basis enables controlled approximation of spectral functions and low-energy transport coefficients from Euclidean correlators without priors.
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Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD
Lattice QCD results show the shear viscosity to entropy density ratio of gluon plasma reaches a minimum near the transition temperature Tc while the bulk viscosity to entropy density ratio decreases monotonically from 0.76 to 2.25 Tc.
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Analytic structure of stress-energy response functions and new Kubo formulae
Authors derive new Kubo formulae for transport coefficients by analyzing analytic structures of stress-energy response functions in second- and third-order hydrodynamics.
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Chiral Magnetic Effect and Negative Magnetoresistance across the phase diagram of finite-density SU(2) gauge theory
In SU(2) lattice QCD at finite density, the chiral magnetic effect from axial-vector correlators remains close to the free massless quark value with weak T and mu dependence in the plasma, while negative magnetoresistance from vector correlators is strongly suppressed at high density or temperature.